Now showing1 - 1 of 1
- Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Super-localized orthogonal decomposition for convection-dominated diffusion problemsThis paper presents a novel multi-scale method for convection-dominated diffusion problems in the regime of large Péclet numbers. The method involves applying the solution operator to piecewise constant right-hand sides on an arbitrary coarse mesh, which defines a finite-dimensional coarse ansatz space with favorable approximation properties. For some relevant error measures, including the L2-norm, the Galerkin projection onto this generalized finite element space even yields ε-independent error bounds, ε being the singular perturbation parameter. By constructing an approximate local basis, the approach becomes a novel multi-scale method in the spirit of the Super-Localized Orthogonal Decomposition (SLOD). The error caused by basis localization can be estimated in an a posteriori way. In contrast to existing multi-scale methods, numerical experiments indicate ε-robust convergence without pre-asymptotic effects even in the under-resolved regime of large mesh Péclet numbers.Publicationtype: Journal Article17 40